Model-Eliciting Activities (MEAs) - The UTeach Institute

Adem Ekmekci & Gladys Krause HANDOUTS UTeach Institute - NMSI Annual Conference
Austin, TX / May 24 – 26, 2011
College Level Students’ Reasoning of an Optimization Problem:
Historic Hotel MEA (Model-Eliciting Activity)
Adem Ekmekci
University of Texas at Austin
ekmekci@mail.utexas.edu
Angeles Domínguez
Instituto Tecnologico de Estudios
Superiores de Monterrey
angeles.dominguez@itesm.mx
Model-eliciting activities (MEAs) are based on real-life situations where students,
working in small groups, present a mathematical model as a solution to a client’s need
(Zawojewski and Carmona, 2001). The problem of Historic Hotels is an MEA in which
students are asked to develop a mathematical model to maximize profit that can be
calculated with a quadratic equation. In the problem, there is a client who inherited a
historic hotel and does not have management skills. He wants to determine the rate per
room where he was told by the previous owner that all of 80 rooms are occupied when
the daily rate is $60 per room; the rate per room increases by $1 for every vacant room;
and each occupied room has a $4 cost for service and maintenance. The problem can be
solved by using quadratic formulas, 1 st and 2 nd derivative method, or simply looking at
the profit for each value. In this study, college level students are asked to solve this
optimization problem to see possible their ways of solution to the problem. Two groups
of students were given this non-traditional problem. The first group was a calculus class
where the majority of students were engineering major and the second one was an
education course required for teaching certification where students were either science or
math major. There were 23 groups of 3 in calculus class and 11 groups of 3 in the other.
After the problem was solved in groups, students were asked to present their
models to their class-mates. Discussions about different solutions were done after each
presentation. Authors and their colleagues observed students and took field notes while
students were working on the problem and discussing their results afterwards. This
particular type of MEA made students’ thinking about optimization as a mathematical
concept visible to both their peers and teachers. Formative assessment (Black & William,
1998) cycles that students went through appeared in the problem solving process.
Students’ final works are analyzed in terms of the function they used, variables and their
definitions, graphical representations, and generalizations.
Analysis of solutions of both groups to the problem and observations by authors
and their colleagues will be reported in the poster. In addition, math major students’ and
pre-service teachers’ ways of thinking will be discussed. Following questions will also be
touched upon in the poster:
- How much calculus knowledge do college level students associate with solving an
optimization problem?
- In what ways, did college level students model the maximization of profit in the
given context?
- What symbols and tool did students use in solving the problem?
- Were there any differences in the method used between calculus students and
students in teacher certification program?
1